No, shorting a dead LED in a series chain of 10-20 will NOT burn your house down, it’s barely a difference to the driving circuit. Unless you’re buying knockoffs, there is a fuse in the base that will blow at like 0.5 A, no matter what you do to the circuitry. However, the other chips will likely not last much longer than the first dead one (unless you dooby the bulb, see below), so it’s not worth doing, and a poorly reattached plastic globe can come off and expose mains voltage. If all chips are OK, you can cut it open to check the inductor between smoothing capacitors and replace it if it has failed open circuit, or short it if you accept a little extra flicker and/or electrical noise.

I’ve seen power supply boards of LED bulbs that literally burned themselves down to the crisp (never in ones that I modded) but the housing contained the fire thanks to its heat-dissipating design.

In many bulbs, you can adjust the value of a current-sensing resistor (usually one or two in parallel, about 2-30 Ω) to make your own “Dooby” lamp with lower power and way longer life. Of course, you need to know something about electronics.

What can burn your house down is still using incandescent and halogen bulbs. You may lay a piece of paper on top of a lamp and it can fall in when moved by the hot air, touching the bulb…